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Year 2016, Volume: 4 Issue: 2, 149 - 157, 01.10.2016

FUAT Usta

Abstract

References

  • [1] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015) 57-66.
  • [2] Douglas R. Anderson and Darin J. Ulness, Newly de ned conformable derivatives, Advances in Dynamical Systems and Applications Vol:10, No.2 (2015), 109-137.
  • [3] C. Franke and R. Schaback, Solving partial differential equations by collocation using radial basis functions, Applied Mathematics and Computation 93 (1998) 73-82.
  • [4] R. L. Hardy, Theory and applications of the multiquadric biharmonic method. 20 years of discovery 1968-1988, Computers and Mathematics with Applications 19(8-9) (1990) 163{208.
  • [5] E. J. Kansa, Multiquadricsa scattered data approximation scheme with applications to computational luid-dynamics. I. Surface approximations and partial derivative estimates, Computers and Mathematics with Applications 19(8-9) (1990) 127{145.
  • [6] U.N. Katugampola, A new fractional derivative with classical properties, Journal of the American Math.Soc., 2014, in press, arXiv:1410.6535.
  • [7] R. Khalil, M. Al horani, A. Yousef and M. Sababheh, A new de nition of fractional derivative, Journal of Computational Applied Mathematics, 264 (2014), 65-70.
  • [8] A. A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier B.V., Amsterdam, Netherlands, 2006.
  • [9] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego CA, 1999.
  • [10] M. J. D. Powell, The theory of radial basis function approximation in 1990, Oxford University Press, New York, 1992.
  • [11] S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordonand Breach, Yverdon et alibi, 1993.
  • [12] Y. Zhang, A nite difference method for fractional partial di erential equation, Applied Mathematics and Computation, Vol:215, No.2 (2009), 524-529.

A MESH-FREE TECHNIQUE OF NUMERICAL SOLUTION OF NEWLY DEFINED CONFORMABLE DIFFERENTIAL EQUATIONS

Year 2016, Volume: 4 Issue: 2, 149 - 157, 01.10.2016

FUAT Usta

Abstract

Motivated by the recently defined conformable derivatives proposed in [2], we introduced a new approach of solving the conformable ordinary differential equation with the mesh-free numerical method. Since radial basis function collocation technique has outstanding feature in comparison with the other numerical methods, we use it to solve non-integer order of differential equation. We subsequently present the results of numerical experimentation to show that our algorithm provide successful consequences.

Keywords

Conformable derivative mesh-less method radial basis functions collocation technique

References

  • [1] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015) 57-66.
  • [2] Douglas R. Anderson and Darin J. Ulness, Newly de ned conformable derivatives, Advances in Dynamical Systems and Applications Vol:10, No.2 (2015), 109-137.
  • [3] C. Franke and R. Schaback, Solving partial differential equations by collocation using radial basis functions, Applied Mathematics and Computation 93 (1998) 73-82.
  • [4] R. L. Hardy, Theory and applications of the multiquadric biharmonic method. 20 years of discovery 1968-1988, Computers and Mathematics with Applications 19(8-9) (1990) 163{208.
  • [5] E. J. Kansa, Multiquadricsa scattered data approximation scheme with applications to computational luid-dynamics. I. Surface approximations and partial derivative estimates, Computers and Mathematics with Applications 19(8-9) (1990) 127{145.
  • [6] U.N. Katugampola, A new fractional derivative with classical properties, Journal of the American Math.Soc., 2014, in press, arXiv:1410.6535.
  • [7] R. Khalil, M. Al horani, A. Yousef and M. Sababheh, A new de nition of fractional derivative, Journal of Computational Applied Mathematics, 264 (2014), 65-70.
  • [8] A. A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier B.V., Amsterdam, Netherlands, 2006.
  • [9] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego CA, 1999.
  • [10] M. J. D. Powell, The theory of radial basis function approximation in 1990, Oxford University Press, New York, 1992.
  • [11] S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordonand Breach, Yverdon et alibi, 1993.
  • [12] Y. Zhang, A nite difference method for fractional partial di erential equation, Applied Mathematics and Computation, Vol:215, No.2 (2009), 524-529.
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

FUAT Usta

Publication Date October 1, 2016
Submission Date July 16, 2015
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Usta, F. (2016). A MESH-FREE TECHNIQUE OF NUMERICAL SOLUTION OF NEWLY DEFINED CONFORMABLE DIFFERENTIAL EQUATIONS. Konuralp Journal of Mathematics, 4(2), 149-157.
AMA Usta F. A MESH-FREE TECHNIQUE OF NUMERICAL SOLUTION OF NEWLY DEFINED CONFORMABLE DIFFERENTIAL EQUATIONS. Konuralp J. Math. October 2016;4(2):149-157.
Chicago Usta, FUAT. “A MESH-FREE TECHNIQUE OF NUMERICAL SOLUTION OF NEWLY DEFINED CONFORMABLE DIFFERENTIAL EQUATIONS”. Konuralp Journal of Mathematics 4, no. 2 (October 2016): 149-57.
EndNote Usta F (October 1, 2016) A MESH-FREE TECHNIQUE OF NUMERICAL SOLUTION OF NEWLY DEFINED CONFORMABLE DIFFERENTIAL EQUATIONS. Konuralp Journal of Mathematics 4 2 149–157.
IEEE F. Usta, “A MESH-FREE TECHNIQUE OF NUMERICAL SOLUTION OF NEWLY DEFINED CONFORMABLE DIFFERENTIAL EQUATIONS”, Konuralp J. Math., vol. 4, no. 2, pp. 149–157, 2016.
ISNAD Usta, FUAT. “A MESH-FREE TECHNIQUE OF NUMERICAL SOLUTION OF NEWLY DEFINED CONFORMABLE DIFFERENTIAL EQUATIONS”. Konuralp Journal of Mathematics 4/2 (October 2016), 149-157.
JAMA Usta F. A MESH-FREE TECHNIQUE OF NUMERICAL SOLUTION OF NEWLY DEFINED CONFORMABLE DIFFERENTIAL EQUATIONS. Konuralp J. Math. 2016;4:149–157.
MLA Usta, FUAT. “A MESH-FREE TECHNIQUE OF NUMERICAL SOLUTION OF NEWLY DEFINED CONFORMABLE DIFFERENTIAL EQUATIONS”. Konuralp Journal of Mathematics, vol. 4, no. 2, 2016, pp. 149-57.
Vancouver Usta F. A MESH-FREE TECHNIQUE OF NUMERICAL SOLUTION OF NEWLY DEFINED CONFORMABLE DIFFERENTIAL EQUATIONS. Konuralp J. Math. 2016;4(2):149-57.
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